And this method can be used for complex numbers in rectangular form, $a+bi$, only when it is converted to polar form. To do this, we use two conversion formulas:

(2)

\begin{align} r=\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \end{align}

(3)

\begin{align} \theta ={ Arctan }\frac { b }{ a } \end{align}

If we use these conversion formulas, we can turn ${ 2+11i }$ and ${ 2-11i }$ into two equivalent complex numbers in polar form: $\sqrt { 125 } cis\left( Arctan\frac { 11 }{ 2 } \right)$ and $\sqrt { 125 } cis\left( Arctan\frac { -11 }{ 2 } \right)$, respectively. Note that the radical is left unreduced (because it's easier to raise to a fractional power) and the angles are left in terms of the Arctans (because they are not integer angles).

Now, to evaluate the two complex numbers to the $\frac { 1 }{ 3 }$ power, we use DeMoivre's Theorem. Therefore: